In the 1990s, the concept of flatness has been introduced by Fliess,
Lévine, Martin and Rouchon for nonlinear continuous-time systems
(see e.g. [1]}, [2]}
and [3]}). Flat continuous-time
systems have the characteristic feature that all system variables
can be parameterized by a flat output and its time derivatives. This
leads to a one-to-one correspondence of solutions of a flat system
to solutions of a trivial system with the same number of inputs. Flat
systems form an extension of the class of static feedback linearizable
systems and can be linearized by an endogenous dynamic feedback. Their
popularity stems from the fact that many physical systems possess
the property of flatness and that the knowledge of a flat output allows
an elegant solution to motion planning problems and a systematic design
of tracking controllers.
